The vertices of triangle ABC are A(2,4), B(7,6) and C(5,2). ABC after a composition of the transformations in the order they are listed. Translation (x,y) into (x-2, y) and Rotation 90 degrees CCW

Answer 1

First, translate the points according to the given information: (x,y) ==> (x-2,y)

This indicates that the triangle is moving two units to the left (in the negative-x direction):

(1) Translation: A(2,4), B(7,6), C(5,2) ==> A(0,4), B(5,6), C(3,2)

Second, rotate the points counter-clockwise (CCW) around the origin of coordinates. When this is done, each positive x-coordinate becomes a positive y-coordinate, and each positive y-coordinate becomes a negative x-coordinate: (x,y) ==> (-y,x)

(2) Rotation 90-degrees CCW: A(0,4), B(5,6), C(3,2) ==> A(-4,0), B(-6,5), C(-2,3)

So the verticies of triangle ABC after both the translation and the rotation are A(-4,0), B(-6,5), C(-2,3)

Answer 2

Translation will reduce x coordinate by 2: (0,4), (5,6) and (3,2)

Rotation 90 CCW will change (x,y) to (-y,x): (-4,0),(-6,5),(-2,3)